14. Sequences & Series

The first 4 terms of a sequence are $\(\left\[\lbrace\]\sqrt\)3,2\(\sqrt\)3,3\(\sqrt\)3,4\(\sqrt\)3,\(\ldots\[\right\]\rbrace\)$. Continuing this pattern, find the $7^{\(\th\)}$ term.

Find the general formula for the arithmetic sequence below. Without using a recursive formula, calculate the $30^{\(\th\)}$ term.

$\(\left\)\(\lbrace\)-9,-4,1,6,\(\ldots\[\right\]\rbrace\)$

Write a recursive formula for the arithmetic sequence.

$\(\left\)\(\lbrace\)8,2,-4,-10,\(\ldots\[\right\]\rbrace\)$

Write a recursive formula for the geometric sequence $\(\left\)\(\lbrace\)18,6,2,\(\frac\)23,\(\ldots\[\right\]\rbrace\)$.

Find the $10^{\(\th\)}$ term of the geometric sequence in which $a_1=5$ and $r=2$.

Write a formula for the general or $n^{\(\th\)}$ term of the geometric sequence where $a_7=1458$ and $r=-3$.

Determine the first 3 terms of the sequence given by the general formula

$a_{n}=\(\frac{1}{n!+1}\)$